New Two-Step Conjugate Gradient Method for Unconstrained Optimization

Moghrabi, Issam A. R.

doi:10.12732/ijam.v33i5.8

Cited by 4 publications

(5 citation statements)

References 30 publications

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“…The comparative tests involve eighteen well-known test functions (see Table 1) obtained from [14], [15], [16], [17]. The comparative performances of the algorithms are assessed by taking into account both the total number of iterations and the number of function evaluations, in addition to computational timings.…”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

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New Invariant to Nonlinear Scaling Quasi-Newton Algorithms

Moghrabi¹

2021

Int. J. of Appl. Math.

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New Quasi-Newton methods for unconstrained optimization are proposed which are invariant to a nonlinear scaling of a strictly convex quadratic function. In specific, we examine a logarithmic scaling of some quadratic function and proceed to derive the necessary parameters for obtaining invariancy to such nonlinear scalings. The techniques considered in this work have the same convergence properties as the classical BFGS-method, when applied to a quadratic function.

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Section: Numerical Results and Conclusionmentioning

confidence: 99%

“…is deemed acceptable provided it satisfies the Wolfe conditions (see [4], [7], [16], [18], [19], and [24])…”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

New Invariant to Nonlinear Scaling Quasi-Newton Algorithms

Moghrabi¹

2021

Int. J. of Appl. Math.

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“…,respectively.Numerically,themost successfulquasi-NewtonmethodistheBFGSmethod (Broyden,1970). Whentheobjectivefunctionfisconvex,globalconvergenceoftheBFGSmethodshasbeen established by some authors (see Byrd, Schnabel and Shultz, 1988;Dai, 2002;Moghrabi, 2019;Tajadod,Abedini,Rategari,&Mobin,2016;Wolfe,1971). Dai(2002)employedillustratedthatthe standardBFGSmethodmayfailonnon-convexfunctionswithinexactlinesearch.…”

Section: ( ) ∈mentioning

confidence: 97%

“…If σ i i H = and ε = 1 , the scalar β i disappears and d i reduces to a memoryless multi-step methodsearchdirectionthatsatisfiestherelationin(4). Moghrabi(2019)proceedswiththechoice σ i i H = .Tocompletetheimplementationdetailsof the algorithm, the quantity d H g…”

Section: ( ) ∈mentioning

confidence: 99%

New Dual Parameter Quasi-Newton Methods for Unconstrained Nonlinear Programs

Moughrabi

Askary

2019

International Journal of Strategic Decision Sciences

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A framework model of multi-step quasi-Newton methods developed which utilizes values of the objective function. The model is constructed using iteration genereted data from the m+1 most recent iterates/gradient evaluations. It hosts double free parameters which introduce a certain degree of flexibility. This permits the interpolating polynomials to exploit available computed function values which are otherwise discarded and left unused. Two new algorithms are derived for those function values incorporated in the update of the inverse Hessian approximation at each iteration to accelerate convergence. The idea of incorporating function values configure quasi-Newton methods, but the presentation constitutes a new approach for such algorithms. Several earlier works only include function values data in the update of the Hessian approximation numerically to improve the convergence of Secant-like methods. The methods are a useful tool for solving nonlinear problems arising in engineering, physics, machine learning, decision science, approximations techniques to Bayesian Regressors and a variety of numerical analysis applications.

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“…Because of the accumulation of round-off errors, orthogonality only really exists for a few adjacent vectors and convergence difficulties are present for large ill-conditioned systems. Many restart [5] and preconditioning techniques [6][7][8][9][10] improve convergence.…”

Section: Non-recursive Cg-like Algorithm Without the Need To Restartmentioning

confidence: 99%

Exact arithmetic as a tool for convergence assessment of the IRM-CG method

Dvornik

Jaguljnjak-Lazarević

Lazarević

et al. 2020

Heliyon

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Exact arithmetic as a tool for convergence assessment of the IRM-CG method This is an author produced version of a paper submitted to a peer-review Exact arithmetic as a tool for convergence assessment of the IRM-CG method AbstractUsing exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by rationalisation of numerically given input data. In the latter case there is an initial roundoff error, but this does not propagate during the solution process. If this system is first exactly solved, then by the floating-point arithmetic, convergence of the numerical method is easily followed. As one example, IRM-CG, a special case of the more general Iterated Ritz method and interesting replacement for a standard or preconditioned CG, is verified. Further, because the computer demands and execution time grow enourmously with the number of unknowns using this strategy, the possibilities for larger systems are also provided.

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New Two-Step Conjugate Gradient Method for Unconstrained Optimization

Cited by 4 publications

References 30 publications

New Invariant to Nonlinear Scaling Quasi-Newton Algorithms

New Invariant to Nonlinear Scaling Quasi-Newton Algorithms

New Dual Parameter Quasi-Newton Methods for Unconstrained Nonlinear Programs

Exact arithmetic as a tool for convergence assessment of the IRM-CG method

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